Question: $\dfrac{d}{dx}\left(\dfrac{1}{x^{12}}\right)=$
Answer: The strategy We can first rewrite the fraction as a negative power of $x$. Then, the derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is negative.) Rewriting the fraction as a negative power $\dfrac{1}{x^{12}}=x^{-12}$ Differentiating using the power rule $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{-12}\right) \\\\ &=-12x^{-12-1} \gray{\text{The power rule}} \\\\ &=-12x^{-13} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(\dfrac{1}{x^{12}}\right)=-12x^{-13}$. This can also be written as $-\dfrac{12}{x^{13}}$ (all equivalent forms are accepted).